Properties

Label 177.10.a.a.1.12
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} -1977.63 q^{10} +70322.7 q^{11} -41273.3 q^{12} -47687.6 q^{13} -11990.2 q^{14} -102272. q^{15} +258382. q^{16} +389608. q^{17} +10276.5 q^{18} +511521. q^{19} +643360. q^{20} -620063. q^{21} +110147. q^{22} +172172. q^{23} -129604. q^{24} -358937. q^{25} -74693.2 q^{26} +531441. q^{27} +3.90063e6 q^{28} +4.84225e6 q^{29} -160188. q^{30} -187258. q^{31} +1.22393e6 q^{32} +5.69613e6 q^{33} +610244. q^{34} +9.66542e6 q^{35} -3.34314e6 q^{36} -2.06095e7 q^{37} +801196. q^{38} -3.86269e6 q^{39} +2.02024e6 q^{40} +1.23789e7 q^{41} -971207. q^{42} -3.93068e7 q^{43} -3.58327e7 q^{44} -8.28400e6 q^{45} +269673. q^{46} -3.33132e7 q^{47} +2.09289e7 q^{48} +1.82470e7 q^{49} -562203. q^{50} +3.15582e7 q^{51} +2.42990e7 q^{52} +1.91650e7 q^{53} +832398. q^{54} -8.87902e7 q^{55} +1.22486e7 q^{56} +4.14332e7 q^{57} +7.58443e6 q^{58} +1.21174e7 q^{59} +5.21121e7 q^{60} -1.21058e8 q^{61} -293303. q^{62} -5.02251e7 q^{63} -1.30374e8 q^{64} +6.02109e7 q^{65} +8.92187e6 q^{66} +2.99688e6 q^{67} -1.98523e8 q^{68} +1.39459e7 q^{69} +1.51390e7 q^{70} -1.08294e8 q^{71} -1.04979e7 q^{72} +7.68824e7 q^{73} -3.22808e7 q^{74} -2.90739e7 q^{75} -2.60644e8 q^{76} -5.38327e8 q^{77} -6.05015e6 q^{78} +3.66431e8 q^{79} -3.26236e8 q^{80} +4.30467e7 q^{81} +1.93891e7 q^{82} +4.97567e8 q^{83} +3.15951e8 q^{84} -4.91924e8 q^{85} -6.15664e7 q^{86} +3.92222e8 q^{87} -1.12520e8 q^{88} +4.74027e8 q^{89} -1.29752e7 q^{90} +3.65053e8 q^{91} -8.77296e7 q^{92} -1.51679e7 q^{93} -5.21785e7 q^{94} -6.45852e8 q^{95} +9.91384e7 q^{96} -3.38070e8 q^{97} +2.85803e7 q^{98} +4.61387e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.56630 0.0692215 0.0346107 0.999401i \(-0.488981\pi\)
0.0346107 + 0.999401i \(0.488981\pi\)
\(3\) 81.0000 0.577350
\(4\) −509.547 −0.995208
\(5\) −1262.61 −0.903451 −0.451726 0.892157i \(-0.649191\pi\)
−0.451726 + 0.892157i \(0.649191\pi\)
\(6\) 126.871 0.0399650
\(7\) −7655.10 −1.20506 −0.602531 0.798095i \(-0.705841\pi\)
−0.602531 + 0.798095i \(0.705841\pi\)
\(8\) −1600.05 −0.138111
\(9\) 6561.00 0.333333
\(10\) −1977.63 −0.0625382
\(11\) 70322.7 1.44820 0.724099 0.689696i \(-0.242256\pi\)
0.724099 + 0.689696i \(0.242256\pi\)
\(12\) −41273.3 −0.574584
\(13\) −47687.6 −0.463084 −0.231542 0.972825i \(-0.574377\pi\)
−0.231542 + 0.972825i \(0.574377\pi\)
\(14\) −11990.2 −0.0834162
\(15\) −102272. −0.521608
\(16\) 258382. 0.985648
\(17\) 389608. 1.13138 0.565689 0.824619i \(-0.308610\pi\)
0.565689 + 0.824619i \(0.308610\pi\)
\(18\) 10276.5 0.0230738
\(19\) 511521. 0.900476 0.450238 0.892909i \(-0.351339\pi\)
0.450238 + 0.892909i \(0.351339\pi\)
\(20\) 643360. 0.899122
\(21\) −620063. −0.695743
\(22\) 110147. 0.100246
\(23\) 172172. 0.128288 0.0641442 0.997941i \(-0.479568\pi\)
0.0641442 + 0.997941i \(0.479568\pi\)
\(24\) −129604. −0.0797386
\(25\) −358937. −0.183776
\(26\) −74693.2 −0.0320554
\(27\) 531441. 0.192450
\(28\) 3.90063e6 1.19929
\(29\) 4.84225e6 1.27132 0.635662 0.771968i \(-0.280727\pi\)
0.635662 + 0.771968i \(0.280727\pi\)
\(30\) −160188. −0.0361065
\(31\) −187258. −0.0364178 −0.0182089 0.999834i \(-0.505796\pi\)
−0.0182089 + 0.999834i \(0.505796\pi\)
\(32\) 1.22393e6 0.206339
\(33\) 5.69613e6 0.836118
\(34\) 610244. 0.0783156
\(35\) 9.66542e6 1.08872
\(36\) −3.34314e6 −0.331736
\(37\) −2.06095e7 −1.80784 −0.903921 0.427700i \(-0.859324\pi\)
−0.903921 + 0.427700i \(0.859324\pi\)
\(38\) 801196. 0.0623322
\(39\) −3.86269e6 −0.267362
\(40\) 2.02024e6 0.124777
\(41\) 1.23789e7 0.684154 0.342077 0.939672i \(-0.388870\pi\)
0.342077 + 0.939672i \(0.388870\pi\)
\(42\) −971207. −0.0481604
\(43\) −3.93068e7 −1.75331 −0.876657 0.481116i \(-0.840232\pi\)
−0.876657 + 0.481116i \(0.840232\pi\)
\(44\) −3.58327e7 −1.44126
\(45\) −8.28400e6 −0.301150
\(46\) 269673. 0.00888030
\(47\) −3.33132e7 −0.995808 −0.497904 0.867232i \(-0.665897\pi\)
−0.497904 + 0.867232i \(0.665897\pi\)
\(48\) 2.09289e7 0.569064
\(49\) 1.82470e7 0.452177
\(50\) −562203. −0.0127212
\(51\) 3.15582e7 0.653201
\(52\) 2.42990e7 0.460865
\(53\) 1.91650e7 0.333632 0.166816 0.985988i \(-0.446651\pi\)
0.166816 + 0.985988i \(0.446651\pi\)
\(54\) 832398. 0.0133217
\(55\) −8.87902e7 −1.30838
\(56\) 1.22486e7 0.166433
\(57\) 4.14332e7 0.519890
\(58\) 7.58443e6 0.0880029
\(59\) 1.21174e7 0.130189
\(60\) 5.21121e7 0.519109
\(61\) −1.21058e8 −1.11946 −0.559730 0.828675i \(-0.689095\pi\)
−0.559730 + 0.828675i \(0.689095\pi\)
\(62\) −293303. −0.00252089
\(63\) −5.02251e7 −0.401688
\(64\) −1.30374e8 −0.971365
\(65\) 6.02109e7 0.418374
\(66\) 8.92187e6 0.0578773
\(67\) 2.99688e6 0.0181691 0.00908455 0.999959i \(-0.497108\pi\)
0.00908455 + 0.999959i \(0.497108\pi\)
\(68\) −1.98523e8 −1.12596
\(69\) 1.39459e7 0.0740673
\(70\) 1.51390e7 0.0753625
\(71\) −1.08294e8 −0.505755 −0.252878 0.967498i \(-0.581377\pi\)
−0.252878 + 0.967498i \(0.581377\pi\)
\(72\) −1.04979e7 −0.0460371
\(73\) 7.68824e7 0.316865 0.158433 0.987370i \(-0.449356\pi\)
0.158433 + 0.987370i \(0.449356\pi\)
\(74\) −3.22808e7 −0.125141
\(75\) −2.90739e7 −0.106103
\(76\) −2.60644e8 −0.896161
\(77\) −5.38327e8 −1.74517
\(78\) −6.05015e6 −0.0185072
\(79\) 3.66431e8 1.05845 0.529225 0.848482i \(-0.322483\pi\)
0.529225 + 0.848482i \(0.322483\pi\)
\(80\) −3.26236e8 −0.890485
\(81\) 4.30467e7 0.111111
\(82\) 1.93891e7 0.0473581
\(83\) 4.97567e8 1.15080 0.575401 0.817872i \(-0.304846\pi\)
0.575401 + 0.817872i \(0.304846\pi\)
\(84\) 3.15951e8 0.692410
\(85\) −4.91924e8 −1.02214
\(86\) −6.15664e7 −0.121367
\(87\) 3.92222e8 0.733999
\(88\) −1.12520e8 −0.200013
\(89\) 4.74027e8 0.800844 0.400422 0.916331i \(-0.368864\pi\)
0.400422 + 0.916331i \(0.368864\pi\)
\(90\) −1.29752e7 −0.0208461
\(91\) 3.65053e8 0.558046
\(92\) −8.77296e7 −0.127674
\(93\) −1.51679e7 −0.0210258
\(94\) −5.21785e7 −0.0689313
\(95\) −6.45852e8 −0.813536
\(96\) 9.91384e7 0.119130
\(97\) −3.38070e8 −0.387734 −0.193867 0.981028i \(-0.562103\pi\)
−0.193867 + 0.981028i \(0.562103\pi\)
\(98\) 2.85803e7 0.0313003
\(99\) 4.61387e8 0.482733
\(100\) 1.82895e8 0.182895
\(101\) 3.15186e8 0.301384 0.150692 0.988581i \(-0.451850\pi\)
0.150692 + 0.988581i \(0.451850\pi\)
\(102\) 4.94298e7 0.0452155
\(103\) −2.29811e7 −0.0201188 −0.0100594 0.999949i \(-0.503202\pi\)
−0.0100594 + 0.999949i \(0.503202\pi\)
\(104\) 7.63025e7 0.0639571
\(105\) 7.82899e8 0.628570
\(106\) 3.00183e7 0.0230945
\(107\) 9.85007e8 0.726461 0.363230 0.931699i \(-0.381674\pi\)
0.363230 + 0.931699i \(0.381674\pi\)
\(108\) −2.70794e8 −0.191528
\(109\) −1.24273e9 −0.843253 −0.421626 0.906770i \(-0.638541\pi\)
−0.421626 + 0.906770i \(0.638541\pi\)
\(110\) −1.39072e8 −0.0905678
\(111\) −1.66937e9 −1.04376
\(112\) −1.97794e9 −1.18777
\(113\) 8.64168e8 0.498592 0.249296 0.968427i \(-0.419801\pi\)
0.249296 + 0.968427i \(0.419801\pi\)
\(114\) 6.48969e7 0.0359875
\(115\) −2.17386e8 −0.115902
\(116\) −2.46735e9 −1.26523
\(117\) −3.12878e8 −0.154361
\(118\) 1.89795e7 0.00901187
\(119\) −2.98249e9 −1.36338
\(120\) 1.63640e8 0.0720399
\(121\) 2.58733e9 1.09728
\(122\) −1.89613e8 −0.0774906
\(123\) 1.00269e9 0.394996
\(124\) 9.54168e7 0.0362433
\(125\) 2.91924e9 1.06948
\(126\) −7.86677e7 −0.0278054
\(127\) −4.00552e9 −1.36629 −0.683145 0.730283i \(-0.739388\pi\)
−0.683145 + 0.730283i \(0.739388\pi\)
\(128\) −8.30858e8 −0.273579
\(129\) −3.18385e9 −1.01228
\(130\) 9.43085e7 0.0289605
\(131\) 4.81457e9 1.42836 0.714178 0.699964i \(-0.246801\pi\)
0.714178 + 0.699964i \(0.246801\pi\)
\(132\) −2.90245e9 −0.832112
\(133\) −3.91574e9 −1.08513
\(134\) 4.69403e6 0.00125769
\(135\) −6.71004e8 −0.173869
\(136\) −6.23393e8 −0.156256
\(137\) −7.36777e9 −1.78687 −0.893436 0.449190i \(-0.851712\pi\)
−0.893436 + 0.449190i \(0.851712\pi\)
\(138\) 2.18435e7 0.00512705
\(139\) −2.19930e9 −0.499709 −0.249855 0.968283i \(-0.580383\pi\)
−0.249855 + 0.968283i \(0.580383\pi\)
\(140\) −4.92498e9 −1.08350
\(141\) −2.69837e9 −0.574930
\(142\) −1.69621e8 −0.0350091
\(143\) −3.35352e9 −0.670638
\(144\) 1.69524e9 0.328549
\(145\) −6.11388e9 −1.14858
\(146\) 1.20421e8 0.0219339
\(147\) 1.47800e9 0.261064
\(148\) 1.05015e10 1.79918
\(149\) −3.43090e9 −0.570255 −0.285128 0.958490i \(-0.592036\pi\)
−0.285128 + 0.958490i \(0.592036\pi\)
\(150\) −4.55385e7 −0.00734459
\(151\) −8.57766e9 −1.34268 −0.671340 0.741149i \(-0.734281\pi\)
−0.671340 + 0.741149i \(0.734281\pi\)
\(152\) −8.18459e8 −0.124366
\(153\) 2.55622e9 0.377126
\(154\) −8.43183e8 −0.120803
\(155\) 2.36434e8 0.0329017
\(156\) 1.96822e9 0.266081
\(157\) 2.32463e9 0.305356 0.152678 0.988276i \(-0.451210\pi\)
0.152678 + 0.988276i \(0.451210\pi\)
\(158\) 5.73942e8 0.0732674
\(159\) 1.55237e9 0.192623
\(160\) −1.54535e9 −0.186417
\(161\) −1.31799e9 −0.154596
\(162\) 6.74242e7 0.00769127
\(163\) −1.53845e10 −1.70702 −0.853510 0.521076i \(-0.825531\pi\)
−0.853510 + 0.521076i \(0.825531\pi\)
\(164\) −6.30761e9 −0.680876
\(165\) −7.19201e9 −0.755392
\(166\) 7.79341e8 0.0796602
\(167\) −3.00233e8 −0.0298699 −0.0149350 0.999888i \(-0.504754\pi\)
−0.0149350 + 0.999888i \(0.504754\pi\)
\(168\) 9.92133e8 0.0960900
\(169\) −8.33040e9 −0.785553
\(170\) −7.70501e8 −0.0707544
\(171\) 3.35609e9 0.300159
\(172\) 2.00287e10 1.74491
\(173\) −1.67251e9 −0.141959 −0.0709794 0.997478i \(-0.522612\pi\)
−0.0709794 + 0.997478i \(0.522612\pi\)
\(174\) 6.14339e8 0.0508085
\(175\) 2.74770e9 0.221461
\(176\) 1.81701e10 1.42741
\(177\) 9.81506e8 0.0751646
\(178\) 7.42469e8 0.0554356
\(179\) −6.15034e9 −0.447776 −0.223888 0.974615i \(-0.571875\pi\)
−0.223888 + 0.974615i \(0.571875\pi\)
\(180\) 4.22108e9 0.299707
\(181\) −8.76056e9 −0.606706 −0.303353 0.952878i \(-0.598106\pi\)
−0.303353 + 0.952878i \(0.598106\pi\)
\(182\) 5.71784e8 0.0386287
\(183\) −9.80568e9 −0.646320
\(184\) −2.75484e8 −0.0177181
\(185\) 2.60218e10 1.63330
\(186\) −2.37575e7 −0.00145544
\(187\) 2.73983e10 1.63846
\(188\) 1.69746e10 0.991036
\(189\) −4.06823e9 −0.231914
\(190\) −1.01160e9 −0.0563141
\(191\) −1.67491e10 −0.910631 −0.455315 0.890330i \(-0.650473\pi\)
−0.455315 + 0.890330i \(0.650473\pi\)
\(192\) −1.05603e10 −0.560818
\(193\) −1.80329e10 −0.935532 −0.467766 0.883852i \(-0.654941\pi\)
−0.467766 + 0.883852i \(0.654941\pi\)
\(194\) −5.29520e8 −0.0268395
\(195\) 4.87708e9 0.241548
\(196\) −9.29768e9 −0.450010
\(197\) −1.37553e10 −0.650686 −0.325343 0.945596i \(-0.605480\pi\)
−0.325343 + 0.945596i \(0.605480\pi\)
\(198\) 7.22672e8 0.0334155
\(199\) 4.32422e9 0.195465 0.0977325 0.995213i \(-0.468841\pi\)
0.0977325 + 0.995213i \(0.468841\pi\)
\(200\) 5.74317e8 0.0253815
\(201\) 2.42748e8 0.0104899
\(202\) 4.93676e8 0.0208622
\(203\) −3.70679e10 −1.53203
\(204\) −1.60804e10 −0.650071
\(205\) −1.56297e10 −0.618100
\(206\) −3.59953e7 −0.00139265
\(207\) 1.12962e9 0.0427628
\(208\) −1.23216e10 −0.456438
\(209\) 3.59715e10 1.30407
\(210\) 1.22626e9 0.0435106
\(211\) 4.13380e10 1.43575 0.717874 0.696173i \(-0.245115\pi\)
0.717874 + 0.696173i \(0.245115\pi\)
\(212\) −9.76548e9 −0.332034
\(213\) −8.77179e9 −0.291998
\(214\) 1.54282e9 0.0502867
\(215\) 4.96292e10 1.58403
\(216\) −8.50333e8 −0.0265795
\(217\) 1.43348e9 0.0438857
\(218\) −1.94649e9 −0.0583712
\(219\) 6.22748e9 0.182942
\(220\) 4.52428e10 1.30211
\(221\) −1.85795e10 −0.523923
\(222\) −2.61474e9 −0.0722504
\(223\) −2.32540e10 −0.629688 −0.314844 0.949143i \(-0.601952\pi\)
−0.314844 + 0.949143i \(0.601952\pi\)
\(224\) −9.36931e9 −0.248652
\(225\) −2.35498e9 −0.0612585
\(226\) 1.35355e9 0.0345132
\(227\) −4.52075e10 −1.13004 −0.565021 0.825077i \(-0.691132\pi\)
−0.565021 + 0.825077i \(0.691132\pi\)
\(228\) −2.11121e10 −0.517399
\(229\) 2.87089e10 0.689853 0.344927 0.938630i \(-0.387904\pi\)
0.344927 + 0.938630i \(0.387904\pi\)
\(230\) −3.40493e8 −0.00802292
\(231\) −4.36045e10 −1.00757
\(232\) −7.74785e9 −0.175584
\(233\) −3.08637e10 −0.686034 −0.343017 0.939329i \(-0.611449\pi\)
−0.343017 + 0.939329i \(0.611449\pi\)
\(234\) −4.90062e8 −0.0106851
\(235\) 4.20616e10 0.899664
\(236\) −6.17436e9 −0.129565
\(237\) 2.96809e10 0.611096
\(238\) −4.67148e9 −0.0943753
\(239\) 8.32138e10 1.64970 0.824849 0.565352i \(-0.191260\pi\)
0.824849 + 0.565352i \(0.191260\pi\)
\(240\) −2.64251e10 −0.514122
\(241\) 8.23801e10 1.57306 0.786531 0.617551i \(-0.211875\pi\)
0.786531 + 0.617551i \(0.211875\pi\)
\(242\) 4.05254e9 0.0759553
\(243\) 3.48678e9 0.0641500
\(244\) 6.16846e10 1.11410
\(245\) −2.30388e10 −0.408520
\(246\) 1.57051e9 0.0273422
\(247\) −2.43932e10 −0.416996
\(248\) 2.99623e8 0.00502970
\(249\) 4.03029e10 0.664415
\(250\) 4.57241e9 0.0740312
\(251\) −5.57439e10 −0.886474 −0.443237 0.896404i \(-0.646170\pi\)
−0.443237 + 0.896404i \(0.646170\pi\)
\(252\) 2.55920e10 0.399763
\(253\) 1.21076e10 0.185787
\(254\) −6.27386e9 −0.0945765
\(255\) −3.98458e10 −0.590136
\(256\) 6.54503e10 0.952428
\(257\) 1.16114e10 0.166030 0.0830150 0.996548i \(-0.473545\pi\)
0.0830150 + 0.996548i \(0.473545\pi\)
\(258\) −4.98688e9 −0.0700713
\(259\) 1.57768e11 2.17856
\(260\) −3.06803e10 −0.416369
\(261\) 3.17700e10 0.423775
\(262\) 7.54107e9 0.0988729
\(263\) −7.57102e10 −0.975784 −0.487892 0.872904i \(-0.662234\pi\)
−0.487892 + 0.872904i \(0.662234\pi\)
\(264\) −9.11411e9 −0.115477
\(265\) −2.41980e10 −0.301421
\(266\) −6.13324e9 −0.0751143
\(267\) 3.83962e10 0.462367
\(268\) −1.52705e9 −0.0180820
\(269\) −4.47812e9 −0.0521448 −0.0260724 0.999660i \(-0.508300\pi\)
−0.0260724 + 0.999660i \(0.508300\pi\)
\(270\) −1.05099e9 −0.0120355
\(271\) −1.93242e10 −0.217640 −0.108820 0.994061i \(-0.534707\pi\)
−0.108820 + 0.994061i \(0.534707\pi\)
\(272\) 1.00668e11 1.11514
\(273\) 2.95693e10 0.322188
\(274\) −1.15402e10 −0.123690
\(275\) −2.52414e10 −0.266143
\(276\) −7.10610e9 −0.0737124
\(277\) −8.11879e10 −0.828576 −0.414288 0.910146i \(-0.635969\pi\)
−0.414288 + 0.910146i \(0.635969\pi\)
\(278\) −3.44476e9 −0.0345906
\(279\) −1.22860e9 −0.0121393
\(280\) −1.54652e10 −0.150364
\(281\) −8.77671e10 −0.839757 −0.419878 0.907580i \(-0.637927\pi\)
−0.419878 + 0.907580i \(0.637927\pi\)
\(282\) −4.22646e9 −0.0397975
\(283\) 3.52404e10 0.326589 0.163295 0.986577i \(-0.447788\pi\)
0.163295 + 0.986577i \(0.447788\pi\)
\(284\) 5.51807e10 0.503332
\(285\) −5.23140e10 −0.469695
\(286\) −5.25262e9 −0.0464225
\(287\) −9.47615e10 −0.824448
\(288\) 8.03021e9 0.0687797
\(289\) 3.32065e10 0.280016
\(290\) −9.57619e9 −0.0795063
\(291\) −2.73837e10 −0.223858
\(292\) −3.91752e10 −0.315347
\(293\) −1.31525e11 −1.04257 −0.521283 0.853384i \(-0.674547\pi\)
−0.521283 + 0.853384i \(0.674547\pi\)
\(294\) 2.31500e9 0.0180713
\(295\) −1.52995e10 −0.117619
\(296\) 3.29763e10 0.249683
\(297\) 3.73723e10 0.278706
\(298\) −5.37382e9 −0.0394739
\(299\) −8.21046e9 −0.0594083
\(300\) 1.48145e10 0.105594
\(301\) 3.00898e11 2.11285
\(302\) −1.34352e10 −0.0929423
\(303\) 2.55300e10 0.174004
\(304\) 1.32168e11 0.887552
\(305\) 1.52849e11 1.01138
\(306\) 4.00381e9 0.0261052
\(307\) −2.24505e10 −0.144246 −0.0721230 0.997396i \(-0.522977\pi\)
−0.0721230 + 0.997396i \(0.522977\pi\)
\(308\) 2.74303e11 1.73681
\(309\) −1.86147e9 −0.0116156
\(310\) 3.70328e8 0.00227750
\(311\) 7.33514e10 0.444618 0.222309 0.974976i \(-0.428641\pi\)
0.222309 + 0.974976i \(0.428641\pi\)
\(312\) 6.18051e9 0.0369257
\(313\) −2.62675e11 −1.54693 −0.773463 0.633842i \(-0.781477\pi\)
−0.773463 + 0.633842i \(0.781477\pi\)
\(314\) 3.64108e9 0.0211372
\(315\) 6.34148e10 0.362905
\(316\) −1.86714e11 −1.05338
\(317\) 3.34297e11 1.85937 0.929685 0.368354i \(-0.120079\pi\)
0.929685 + 0.368354i \(0.120079\pi\)
\(318\) 2.43148e9 0.0133336
\(319\) 3.40520e11 1.84113
\(320\) 1.64612e11 0.877581
\(321\) 7.97855e10 0.419422
\(322\) −2.06438e9 −0.0107013
\(323\) 1.99292e11 1.01878
\(324\) −2.19343e10 −0.110579
\(325\) 1.71168e10 0.0851035
\(326\) −2.40968e10 −0.118162
\(327\) −1.00661e11 −0.486852
\(328\) −1.98068e10 −0.0944893
\(329\) 2.55016e11 1.20001
\(330\) −1.12649e10 −0.0522893
\(331\) 7.00734e10 0.320869 0.160434 0.987047i \(-0.448710\pi\)
0.160434 + 0.987047i \(0.448710\pi\)
\(332\) −2.53534e11 −1.14529
\(333\) −1.35219e11 −0.602614
\(334\) −4.70256e8 −0.00206764
\(335\) −3.78390e9 −0.0164149
\(336\) −1.60213e11 −0.685758
\(337\) −2.08582e11 −0.880931 −0.440466 0.897769i \(-0.645187\pi\)
−0.440466 + 0.897769i \(0.645187\pi\)
\(338\) −1.30479e10 −0.0543771
\(339\) 6.99976e10 0.287862
\(340\) 2.50658e11 1.01725
\(341\) −1.31685e10 −0.0527401
\(342\) 5.25665e9 0.0207774
\(343\) 1.69229e11 0.660161
\(344\) 6.28929e10 0.242152
\(345\) −1.76083e10 −0.0669162
\(346\) −2.61966e9 −0.00982659
\(347\) −1.07644e11 −0.398574 −0.199287 0.979941i \(-0.563863\pi\)
−0.199287 + 0.979941i \(0.563863\pi\)
\(348\) −1.99856e11 −0.730482
\(349\) −1.72136e11 −0.621093 −0.310547 0.950558i \(-0.600512\pi\)
−0.310547 + 0.950558i \(0.600512\pi\)
\(350\) 4.30372e9 0.0153299
\(351\) −2.53431e10 −0.0891206
\(352\) 8.60700e10 0.298820
\(353\) −4.23810e11 −1.45273 −0.726365 0.687309i \(-0.758792\pi\)
−0.726365 + 0.687309i \(0.758792\pi\)
\(354\) 1.53734e9 0.00520300
\(355\) 1.36733e11 0.456925
\(356\) −2.41539e11 −0.797006
\(357\) −2.41582e11 −0.787149
\(358\) −9.63329e9 −0.0309957
\(359\) 1.84294e11 0.585579 0.292790 0.956177i \(-0.405416\pi\)
0.292790 + 0.956177i \(0.405416\pi\)
\(360\) 1.32548e10 0.0415923
\(361\) −6.10344e10 −0.189144
\(362\) −1.37217e10 −0.0419971
\(363\) 2.09574e11 0.633515
\(364\) −1.86012e11 −0.555372
\(365\) −9.70727e10 −0.286272
\(366\) −1.53587e10 −0.0447392
\(367\) −5.29663e11 −1.52406 −0.762031 0.647540i \(-0.775798\pi\)
−0.762031 + 0.647540i \(0.775798\pi\)
\(368\) 4.44861e10 0.126447
\(369\) 8.12178e10 0.228051
\(370\) 4.07581e10 0.113059
\(371\) −1.46710e11 −0.402048
\(372\) 7.72876e9 0.0209251
\(373\) 4.37611e11 1.17057 0.585286 0.810827i \(-0.300982\pi\)
0.585286 + 0.810827i \(0.300982\pi\)
\(374\) 4.29140e10 0.113417
\(375\) 2.36458e11 0.617467
\(376\) 5.33028e10 0.137532
\(377\) −2.30915e11 −0.588730
\(378\) −6.37209e9 −0.0160535
\(379\) −5.01861e11 −1.24942 −0.624708 0.780858i \(-0.714782\pi\)
−0.624708 + 0.780858i \(0.714782\pi\)
\(380\) 3.29092e11 0.809638
\(381\) −3.24447e11 −0.788827
\(382\) −2.62342e10 −0.0630352
\(383\) −4.53506e11 −1.07693 −0.538467 0.842647i \(-0.680996\pi\)
−0.538467 + 0.842647i \(0.680996\pi\)
\(384\) −6.72995e10 −0.157951
\(385\) 6.79698e11 1.57668
\(386\) −2.82450e10 −0.0647589
\(387\) −2.57892e11 −0.584438
\(388\) 1.72262e11 0.385876
\(389\) −2.98127e11 −0.660128 −0.330064 0.943958i \(-0.607070\pi\)
−0.330064 + 0.943958i \(0.607070\pi\)
\(390\) 7.63899e9 0.0167203
\(391\) 6.70796e10 0.145143
\(392\) −2.91961e10 −0.0624507
\(393\) 3.89980e11 0.824662
\(394\) −2.15450e10 −0.0450415
\(395\) −4.62660e11 −0.956258
\(396\) −2.35098e11 −0.480420
\(397\) −4.25238e11 −0.859161 −0.429581 0.903029i \(-0.641339\pi\)
−0.429581 + 0.903029i \(0.641339\pi\)
\(398\) 6.77304e9 0.0135304
\(399\) −3.17175e11 −0.626500
\(400\) −9.27427e10 −0.181138
\(401\) −8.08814e10 −0.156207 −0.0781033 0.996945i \(-0.524886\pi\)
−0.0781033 + 0.996945i \(0.524886\pi\)
\(402\) 3.80216e8 0.000726128 0
\(403\) 8.92988e9 0.0168645
\(404\) −1.60602e11 −0.299940
\(405\) −5.43513e10 −0.100383
\(406\) −5.80596e10 −0.106049
\(407\) −1.44932e12 −2.61811
\(408\) −5.04948e10 −0.0902144
\(409\) 9.44992e11 1.66983 0.834917 0.550376i \(-0.185516\pi\)
0.834917 + 0.550376i \(0.185516\pi\)
\(410\) −2.44809e10 −0.0427858
\(411\) −5.96789e11 −1.03165
\(412\) 1.17099e10 0.0200224
\(413\) −9.27596e10 −0.156886
\(414\) 1.76933e9 0.00296010
\(415\) −6.28234e11 −1.03969
\(416\) −5.83663e10 −0.0955525
\(417\) −1.78143e11 −0.288507
\(418\) 5.63422e10 0.0902695
\(419\) −5.00997e11 −0.794095 −0.397047 0.917798i \(-0.629965\pi\)
−0.397047 + 0.917798i \(0.629965\pi\)
\(420\) −3.98924e11 −0.625559
\(421\) 3.45900e11 0.536637 0.268319 0.963330i \(-0.413532\pi\)
0.268319 + 0.963330i \(0.413532\pi\)
\(422\) 6.47478e10 0.0993846
\(423\) −2.18568e11 −0.331936
\(424\) −3.06650e10 −0.0460784
\(425\) −1.39845e11 −0.207920
\(426\) −1.37393e10 −0.0202125
\(427\) 9.26709e11 1.34902
\(428\) −5.01907e11 −0.722980
\(429\) −2.71635e11 −0.387193
\(430\) 7.77344e10 0.109649
\(431\) −1.75665e11 −0.245210 −0.122605 0.992456i \(-0.539125\pi\)
−0.122605 + 0.992456i \(0.539125\pi\)
\(432\) 1.37315e11 0.189688
\(433\) 1.69288e11 0.231436 0.115718 0.993282i \(-0.463083\pi\)
0.115718 + 0.993282i \(0.463083\pi\)
\(434\) 2.24526e9 0.00303783
\(435\) −4.95224e11 −0.663133
\(436\) 6.33229e11 0.839212
\(437\) 8.80695e10 0.115520
\(438\) 9.75412e9 0.0126635
\(439\) 1.27660e12 1.64045 0.820226 0.572039i \(-0.193848\pi\)
0.820226 + 0.572039i \(0.193848\pi\)
\(440\) 1.42069e11 0.180702
\(441\) 1.19718e11 0.150726
\(442\) −2.91010e10 −0.0362667
\(443\) −8.36857e11 −1.03237 −0.516184 0.856478i \(-0.672648\pi\)
−0.516184 + 0.856478i \(0.672648\pi\)
\(444\) 8.50623e11 1.03876
\(445\) −5.98512e11 −0.723523
\(446\) −3.64228e10 −0.0435879
\(447\) −2.77903e11 −0.329237
\(448\) 9.98029e11 1.17056
\(449\) 8.15501e11 0.946926 0.473463 0.880814i \(-0.343004\pi\)
0.473463 + 0.880814i \(0.343004\pi\)
\(450\) −3.68862e9 −0.00424040
\(451\) 8.70515e11 0.990791
\(452\) −4.40334e11 −0.496203
\(453\) −6.94791e11 −0.775197
\(454\) −7.08086e10 −0.0782231
\(455\) −4.60920e11 −0.504167
\(456\) −6.62952e10 −0.0718026
\(457\) 1.19348e12 1.27995 0.639976 0.768395i \(-0.278944\pi\)
0.639976 + 0.768395i \(0.278944\pi\)
\(458\) 4.49668e10 0.0477526
\(459\) 2.07054e11 0.217734
\(460\) 1.10768e11 0.115347
\(461\) −1.82587e12 −1.88285 −0.941427 0.337217i \(-0.890514\pi\)
−0.941427 + 0.337217i \(0.890514\pi\)
\(462\) −6.82978e10 −0.0697458
\(463\) −1.63020e11 −0.164864 −0.0824322 0.996597i \(-0.526269\pi\)
−0.0824322 + 0.996597i \(0.526269\pi\)
\(464\) 1.25115e12 1.25308
\(465\) 1.91512e10 0.0189958
\(466\) −4.83419e10 −0.0474883
\(467\) 7.89092e11 0.767718 0.383859 0.923392i \(-0.374595\pi\)
0.383859 + 0.923392i \(0.374595\pi\)
\(468\) 1.59426e11 0.153622
\(469\) −2.29414e10 −0.0218949
\(470\) 6.58812e10 0.0622761
\(471\) 1.88295e11 0.176297
\(472\) −1.93884e10 −0.0179806
\(473\) −2.76416e12 −2.53915
\(474\) 4.64893e10 0.0423010
\(475\) −1.83603e11 −0.165485
\(476\) 1.51972e12 1.35685
\(477\) 1.25742e11 0.111211
\(478\) 1.30338e11 0.114195
\(479\) 1.31506e12 1.14140 0.570699 0.821159i \(-0.306672\pi\)
0.570699 + 0.821159i \(0.306672\pi\)
\(480\) −1.25173e11 −0.107628
\(481\) 9.82818e11 0.837183
\(482\) 1.29032e11 0.108890
\(483\) −1.06757e11 −0.0892558
\(484\) −1.31836e12 −1.09202
\(485\) 4.26851e11 0.350299
\(486\) 5.46136e9 0.00444056
\(487\) −9.35122e11 −0.753335 −0.376667 0.926349i \(-0.622930\pi\)
−0.376667 + 0.926349i \(0.622930\pi\)
\(488\) 1.93699e11 0.154610
\(489\) −1.24614e12 −0.985549
\(490\) −3.60858e10 −0.0282783
\(491\) −1.15701e12 −0.898404 −0.449202 0.893430i \(-0.648292\pi\)
−0.449202 + 0.893430i \(0.648292\pi\)
\(492\) −5.10917e11 −0.393104
\(493\) 1.88658e12 1.43835
\(494\) −3.82071e10 −0.0288651
\(495\) −5.82553e11 −0.436126
\(496\) −4.83841e10 −0.0358951
\(497\) 8.28999e11 0.609467
\(498\) 6.31266e10 0.0459918
\(499\) 7.24363e11 0.523002 0.261501 0.965203i \(-0.415782\pi\)
0.261501 + 0.965203i \(0.415782\pi\)
\(500\) −1.48749e12 −1.06436
\(501\) −2.43189e10 −0.0172454
\(502\) −8.73119e10 −0.0613630
\(503\) 2.19638e12 1.52986 0.764929 0.644115i \(-0.222774\pi\)
0.764929 + 0.644115i \(0.222774\pi\)
\(504\) 8.03628e10 0.0554776
\(505\) −3.97957e11 −0.272286
\(506\) 1.89641e10 0.0128604
\(507\) −6.74762e11 −0.453539
\(508\) 2.04100e12 1.35974
\(509\) −2.72117e12 −1.79691 −0.898453 0.439070i \(-0.855308\pi\)
−0.898453 + 0.439070i \(0.855308\pi\)
\(510\) −6.24106e10 −0.0408500
\(511\) −5.88543e11 −0.381842
\(512\) 5.27914e11 0.339507
\(513\) 2.71843e11 0.173297
\(514\) 1.81870e10 0.0114928
\(515\) 2.90161e10 0.0181764
\(516\) 1.62232e12 1.00743
\(517\) −2.34267e12 −1.44213
\(518\) 2.47113e11 0.150803
\(519\) −1.35474e11 −0.0819599
\(520\) −9.63405e10 −0.0577822
\(521\) −2.05716e12 −1.22320 −0.611602 0.791166i \(-0.709475\pi\)
−0.611602 + 0.791166i \(0.709475\pi\)
\(522\) 4.97614e10 0.0293343
\(523\) 3.46063e11 0.202254 0.101127 0.994874i \(-0.467755\pi\)
0.101127 + 0.994874i \(0.467755\pi\)
\(524\) −2.45325e12 −1.42151
\(525\) 2.22563e11 0.127861
\(526\) −1.18585e11 −0.0675452
\(527\) −7.29573e10 −0.0412022
\(528\) 1.47178e12 0.824118
\(529\) −1.77151e12 −0.983542
\(530\) −3.79014e10 −0.0208648
\(531\) 7.95020e10 0.0433963
\(532\) 1.99525e12 1.07993
\(533\) −5.90318e11 −0.316821
\(534\) 6.01400e10 0.0320057
\(535\) −1.24368e12 −0.656322
\(536\) −4.79517e9 −0.00250936
\(537\) −4.98178e11 −0.258523
\(538\) −7.01410e9 −0.00360954
\(539\) 1.28317e12 0.654842
\(540\) 3.41908e11 0.173036
\(541\) −2.55356e12 −1.28162 −0.640808 0.767701i \(-0.721401\pi\)
−0.640808 + 0.767701i \(0.721401\pi\)
\(542\) −3.02675e10 −0.0150654
\(543\) −7.09605e11 −0.350282
\(544\) 4.76853e11 0.233448
\(545\) 1.56909e12 0.761838
\(546\) 4.63145e10 0.0223023
\(547\) 1.49657e12 0.714752 0.357376 0.933961i \(-0.383672\pi\)
0.357376 + 0.933961i \(0.383672\pi\)
\(548\) 3.75422e12 1.77831
\(549\) −7.94260e11 −0.373153
\(550\) −3.95356e10 −0.0184228
\(551\) 2.47691e12 1.14480
\(552\) −2.23142e10 −0.0102295
\(553\) −2.80507e12 −1.27550
\(554\) −1.27165e11 −0.0573553
\(555\) 2.10777e12 0.942984
\(556\) 1.12064e12 0.497315
\(557\) −3.27414e12 −1.44128 −0.720641 0.693308i \(-0.756153\pi\)
−0.720641 + 0.693308i \(0.756153\pi\)
\(558\) −1.92436e9 −0.000840297 0
\(559\) 1.87445e12 0.811932
\(560\) 2.49737e12 1.07309
\(561\) 2.21926e12 0.945965
\(562\) −1.37470e11 −0.0581292
\(563\) 2.88899e12 1.21188 0.605938 0.795512i \(-0.292798\pi\)
0.605938 + 0.795512i \(0.292798\pi\)
\(564\) 1.37494e12 0.572175
\(565\) −1.09111e12 −0.450453
\(566\) 5.51972e10 0.0226070
\(567\) −3.29527e11 −0.133896
\(568\) 1.73275e11 0.0698505
\(569\) 2.95747e12 1.18281 0.591405 0.806375i \(-0.298574\pi\)
0.591405 + 0.806375i \(0.298574\pi\)
\(570\) −8.19396e10 −0.0325130
\(571\) 3.90974e12 1.53917 0.769584 0.638546i \(-0.220464\pi\)
0.769584 + 0.638546i \(0.220464\pi\)
\(572\) 1.70877e12 0.667425
\(573\) −1.35668e12 −0.525753
\(574\) −1.48425e11 −0.0570695
\(575\) −6.17988e10 −0.0235763
\(576\) −8.55386e11 −0.323788
\(577\) −2.05289e12 −0.771036 −0.385518 0.922700i \(-0.625977\pi\)
−0.385518 + 0.922700i \(0.625977\pi\)
\(578\) 5.20114e10 0.0193831
\(579\) −1.46067e12 −0.540129
\(580\) 3.11531e12 1.14308
\(581\) −3.80893e12 −1.38679
\(582\) −4.28911e10 −0.0154958
\(583\) 1.34774e12 0.483166
\(584\) −1.23016e11 −0.0437626
\(585\) 3.95044e11 0.139458
\(586\) −2.06008e11 −0.0721680
\(587\) 1.06817e12 0.371336 0.185668 0.982612i \(-0.440555\pi\)
0.185668 + 0.982612i \(0.440555\pi\)
\(588\) −7.53112e11 −0.259813
\(589\) −9.57864e10 −0.0327933
\(590\) −2.39637e10 −0.00814178
\(591\) −1.11418e12 −0.375674
\(592\) −5.32513e12 −1.78190
\(593\) 4.14756e11 0.137736 0.0688679 0.997626i \(-0.478061\pi\)
0.0688679 + 0.997626i \(0.478061\pi\)
\(594\) 5.85364e10 0.0192924
\(595\) 3.76572e12 1.23175
\(596\) 1.74820e12 0.567523
\(597\) 3.50262e11 0.112852
\(598\) −1.28601e10 −0.00411233
\(599\) 3.83346e12 1.21666 0.608331 0.793683i \(-0.291839\pi\)
0.608331 + 0.793683i \(0.291839\pi\)
\(600\) 4.65197e10 0.0146540
\(601\) −3.57132e11 −0.111659 −0.0558295 0.998440i \(-0.517780\pi\)
−0.0558295 + 0.998440i \(0.517780\pi\)
\(602\) 4.71297e11 0.146255
\(603\) 1.96626e10 0.00605636
\(604\) 4.37072e12 1.33625
\(605\) −3.26679e12 −0.991339
\(606\) 3.99878e10 0.0120448
\(607\) 4.67518e12 1.39781 0.698906 0.715213i \(-0.253670\pi\)
0.698906 + 0.715213i \(0.253670\pi\)
\(608\) 6.26066e11 0.185803
\(609\) −3.00250e12 −0.884515
\(610\) 2.39408e11 0.0700090
\(611\) 1.58862e12 0.461143
\(612\) −1.30251e12 −0.375319
\(613\) 6.41882e12 1.83604 0.918022 0.396530i \(-0.129786\pi\)
0.918022 + 0.396530i \(0.129786\pi\)
\(614\) −3.51643e10 −0.00998493
\(615\) −1.26601e12 −0.356860
\(616\) 8.61351e11 0.241028
\(617\) 7.98940e11 0.221938 0.110969 0.993824i \(-0.464605\pi\)
0.110969 + 0.993824i \(0.464605\pi\)
\(618\) −2.91562e9 −0.000804049 0
\(619\) −2.64407e12 −0.723877 −0.361938 0.932202i \(-0.617885\pi\)
−0.361938 + 0.932202i \(0.617885\pi\)
\(620\) −1.20474e11 −0.0327440
\(621\) 9.14992e10 0.0246891
\(622\) 1.14890e11 0.0307771
\(623\) −3.62872e12 −0.965067
\(624\) −9.98049e11 −0.263525
\(625\) −2.98481e12 −0.782451
\(626\) −4.11429e11 −0.107080
\(627\) 2.91369e12 0.752904
\(628\) −1.18451e12 −0.303892
\(629\) −8.02964e12 −2.04535
\(630\) 9.93268e10 0.0251208
\(631\) −6.50229e12 −1.63281 −0.816403 0.577483i \(-0.804035\pi\)
−0.816403 + 0.577483i \(0.804035\pi\)
\(632\) −5.86308e11 −0.146184
\(633\) 3.34838e12 0.828930
\(634\) 5.23611e11 0.128708
\(635\) 5.05742e12 1.23438
\(636\) −7.91004e11 −0.191700
\(637\) −8.70153e11 −0.209396
\(638\) 5.33357e11 0.127446
\(639\) −7.10515e11 −0.168585
\(640\) 1.04905e12 0.247165
\(641\) −1.12461e12 −0.263111 −0.131556 0.991309i \(-0.541997\pi\)
−0.131556 + 0.991309i \(0.541997\pi\)
\(642\) 1.24968e11 0.0290330
\(643\) −3.47734e12 −0.802228 −0.401114 0.916028i \(-0.631377\pi\)
−0.401114 + 0.916028i \(0.631377\pi\)
\(644\) 6.71579e11 0.153855
\(645\) 4.01997e12 0.914543
\(646\) 3.12152e11 0.0705213
\(647\) 1.55048e12 0.347855 0.173927 0.984758i \(-0.444354\pi\)
0.173927 + 0.984758i \(0.444354\pi\)
\(648\) −6.88770e10 −0.0153457
\(649\) 8.52125e11 0.188539
\(650\) 2.68101e10 0.00589099
\(651\) 1.16112e11 0.0253374
\(652\) 7.83911e12 1.69884
\(653\) 6.59037e12 1.41840 0.709202 0.705005i \(-0.249055\pi\)
0.709202 + 0.705005i \(0.249055\pi\)
\(654\) −1.57666e11 −0.0337006
\(655\) −6.07893e12 −1.29045
\(656\) 3.19847e12 0.674335
\(657\) 5.04426e11 0.105622
\(658\) 3.99432e11 0.0830665
\(659\) 4.86030e12 1.00387 0.501937 0.864904i \(-0.332621\pi\)
0.501937 + 0.864904i \(0.332621\pi\)
\(660\) 3.66466e12 0.751772
\(661\) −3.92824e12 −0.800372 −0.400186 0.916434i \(-0.631055\pi\)
−0.400186 + 0.916434i \(0.631055\pi\)
\(662\) 1.09756e11 0.0222110
\(663\) −1.50494e12 −0.302487
\(664\) −7.96133e11 −0.158939
\(665\) 4.94406e12 0.980362
\(666\) −2.11794e11 −0.0417138
\(667\) 8.33700e11 0.163096
\(668\) 1.52983e11 0.0297268
\(669\) −1.88357e12 −0.363551
\(670\) −5.92673e9 −0.00113626
\(671\) −8.51310e12 −1.62120
\(672\) −7.58914e11 −0.143559
\(673\) −6.51980e12 −1.22509 −0.612543 0.790438i \(-0.709853\pi\)
−0.612543 + 0.790438i \(0.709853\pi\)
\(674\) −3.26702e11 −0.0609794
\(675\) −1.90754e11 −0.0353676
\(676\) 4.24473e12 0.781789
\(677\) −5.00751e12 −0.916163 −0.458082 0.888910i \(-0.651463\pi\)
−0.458082 + 0.888910i \(0.651463\pi\)
\(678\) 1.09637e11 0.0199262
\(679\) 2.58796e12 0.467244
\(680\) 7.87103e11 0.141170
\(681\) −3.66181e12 −0.652429
\(682\) −2.06258e10 −0.00365075
\(683\) 9.04640e12 1.59068 0.795340 0.606164i \(-0.207292\pi\)
0.795340 + 0.606164i \(0.207292\pi\)
\(684\) −1.71008e12 −0.298720
\(685\) 9.30263e12 1.61435
\(686\) 2.65063e11 0.0456973
\(687\) 2.32542e12 0.398287
\(688\) −1.01562e13 −1.72815
\(689\) −9.13934e11 −0.154500
\(690\) −2.75799e10 −0.00463204
\(691\) −2.16278e12 −0.360879 −0.180439 0.983586i \(-0.557752\pi\)
−0.180439 + 0.983586i \(0.557752\pi\)
\(692\) 8.52224e11 0.141279
\(693\) −3.53196e12 −0.581724
\(694\) −1.68604e11 −0.0275898
\(695\) 2.77686e12 0.451463
\(696\) −6.27576e11 −0.101374
\(697\) 4.82291e12 0.774036
\(698\) −2.69617e11 −0.0429930
\(699\) −2.49996e12 −0.396082
\(700\) −1.40008e12 −0.220400
\(701\) −5.76596e12 −0.901864 −0.450932 0.892558i \(-0.648908\pi\)
−0.450932 + 0.892558i \(0.648908\pi\)
\(702\) −3.96950e10 −0.00616906
\(703\) −1.05422e13 −1.62792
\(704\) −9.16827e12 −1.40673
\(705\) 3.40699e12 0.519421
\(706\) −6.63815e11 −0.100560
\(707\) −2.41278e12 −0.363187
\(708\) −5.00123e11 −0.0748044
\(709\) 6.21591e12 0.923839 0.461920 0.886922i \(-0.347161\pi\)
0.461920 + 0.886922i \(0.347161\pi\)
\(710\) 2.14165e11 0.0316290
\(711\) 2.40415e12 0.352817
\(712\) −7.58467e11 −0.110606
\(713\) −3.22406e10 −0.00467197
\(714\) −3.78390e11 −0.0544876
\(715\) 4.23419e12 0.605889
\(716\) 3.13389e12 0.445630
\(717\) 6.74032e12 0.952454
\(718\) 2.88660e11 0.0405347
\(719\) −4.25926e12 −0.594367 −0.297183 0.954820i \(-0.596047\pi\)
−0.297183 + 0.954820i \(0.596047\pi\)
\(720\) −2.14043e12 −0.296828
\(721\) 1.75922e11 0.0242444
\(722\) −9.55983e10 −0.0130928
\(723\) 6.67279e12 0.908207
\(724\) 4.46391e12 0.603799
\(725\) −1.73806e12 −0.233638
\(726\) 3.28256e11 0.0438528
\(727\) −1.28038e13 −1.69994 −0.849970 0.526831i \(-0.823380\pi\)
−0.849970 + 0.526831i \(0.823380\pi\)
\(728\) −5.84104e11 −0.0770724
\(729\) 2.82430e11 0.0370370
\(730\) −1.52045e11 −0.0198162
\(731\) −1.53142e13 −1.98366
\(732\) 4.99645e12 0.643223
\(733\) −1.18736e13 −1.51919 −0.759597 0.650394i \(-0.774604\pi\)
−0.759597 + 0.650394i \(0.774604\pi\)
\(734\) −8.29613e11 −0.105498
\(735\) −1.86615e12 −0.235859
\(736\) 2.10726e11 0.0264709
\(737\) 2.10749e11 0.0263125
\(738\) 1.27212e11 0.0157860
\(739\) 5.84625e11 0.0721070 0.0360535 0.999350i \(-0.488521\pi\)
0.0360535 + 0.999350i \(0.488521\pi\)
\(740\) −1.32593e13 −1.62547
\(741\) −1.97585e12 −0.240753
\(742\) −2.29793e11 −0.0278304
\(743\) 1.47498e13 1.77557 0.887784 0.460261i \(-0.152244\pi\)
0.887784 + 0.460261i \(0.152244\pi\)
\(744\) 2.42694e10 0.00290390
\(745\) 4.33189e12 0.515198
\(746\) 6.85431e11 0.0810287
\(747\) 3.26454e12 0.383600
\(748\) −1.39607e13 −1.63061
\(749\) −7.54032e12 −0.875431
\(750\) 3.70365e11 0.0427419
\(751\) −6.15776e12 −0.706388 −0.353194 0.935550i \(-0.614904\pi\)
−0.353194 + 0.935550i \(0.614904\pi\)
\(752\) −8.60751e12 −0.981516
\(753\) −4.51526e12 −0.511806
\(754\) −3.61683e11 −0.0407528
\(755\) 1.08303e13 1.21305
\(756\) 2.07296e12 0.230803
\(757\) −2.91598e11 −0.0322740 −0.0161370 0.999870i \(-0.505137\pi\)
−0.0161370 + 0.999870i \(0.505137\pi\)
\(758\) −7.86067e11 −0.0864864
\(759\) 9.80715e11 0.107264
\(760\) 1.03340e12 0.112358
\(761\) −1.10879e13 −1.19844 −0.599222 0.800583i \(-0.704523\pi\)
−0.599222 + 0.800583i \(0.704523\pi\)
\(762\) −5.08183e11 −0.0546038
\(763\) 9.51323e12 1.01617
\(764\) 8.53447e12 0.906267
\(765\) −3.22751e12 −0.340715
\(766\) −7.10328e11 −0.0745469
\(767\) −5.77847e11 −0.0602884
\(768\) 5.30148e12 0.549884
\(769\) 1.71448e13 1.76792 0.883962 0.467559i \(-0.154866\pi\)
0.883962 + 0.467559i \(0.154866\pi\)
\(770\) 1.06461e12 0.109140
\(771\) 9.40525e11 0.0958574
\(772\) 9.18862e12 0.931049
\(773\) −8.64430e12 −0.870808 −0.435404 0.900235i \(-0.643394\pi\)
−0.435404 + 0.900235i \(0.643394\pi\)
\(774\) −4.03937e11 −0.0404557
\(775\) 6.72138e10 0.00669269
\(776\) 5.40929e11 0.0535504
\(777\) 1.27792e13 1.25779
\(778\) −4.66958e11 −0.0456951
\(779\) 6.33205e12 0.616064
\(780\) −2.48510e12 −0.240391
\(781\) −7.61550e12 −0.732434
\(782\) 1.05067e11 0.0100470
\(783\) 2.57337e12 0.244666
\(784\) 4.71468e12 0.445687
\(785\) −2.93511e12 −0.275874
\(786\) 6.10827e11 0.0570843
\(787\) −2.01047e13 −1.86815 −0.934076 0.357075i \(-0.883774\pi\)
−0.934076 + 0.357075i \(0.883774\pi\)
\(788\) 7.00896e12 0.647569
\(789\) −6.13253e12 −0.563369
\(790\) −7.24666e11 −0.0661936
\(791\) −6.61529e12 −0.600834
\(792\) −7.38243e11 −0.0666708
\(793\) 5.77295e12 0.518404
\(794\) −6.66051e11 −0.0594724
\(795\) −1.96004e12 −0.174025
\(796\) −2.20339e12 −0.194528
\(797\) 4.09905e12 0.359850 0.179925 0.983680i \(-0.442415\pi\)
0.179925 + 0.983680i \(0.442415\pi\)
\(798\) −4.96792e11 −0.0433672
\(799\) −1.29791e13 −1.12663
\(800\) −4.39313e11 −0.0379201
\(801\) 3.11009e12 0.266948
\(802\) −1.26685e11 −0.0108128
\(803\) 5.40658e12 0.458884
\(804\) −1.23691e11 −0.0104397
\(805\) 1.66411e12 0.139670
\(806\) 1.39869e10 0.00116738
\(807\) −3.62728e11 −0.0301058
\(808\) −5.04313e11 −0.0416245
\(809\) 8.96580e12 0.735903 0.367952 0.929845i \(-0.380059\pi\)
0.367952 + 0.929845i \(0.380059\pi\)
\(810\) −8.51306e10 −0.00694869
\(811\) −1.92603e13 −1.56340 −0.781699 0.623656i \(-0.785647\pi\)
−0.781699 + 0.623656i \(0.785647\pi\)
\(812\) 1.88878e13 1.52468
\(813\) −1.56526e12 −0.125655
\(814\) −2.27007e12 −0.181230
\(815\) 1.94246e13 1.54221
\(816\) 8.15407e12 0.643827
\(817\) −2.01062e13 −1.57882
\(818\) 1.48014e12 0.115588
\(819\) 2.39511e12 0.186015
\(820\) 7.96407e12 0.615138
\(821\) −1.71082e13 −1.31419 −0.657096 0.753807i \(-0.728215\pi\)
−0.657096 + 0.753807i \(0.728215\pi\)
\(822\) −9.34753e11 −0.0714124
\(823\) −1.41958e13 −1.07860 −0.539301 0.842113i \(-0.681311\pi\)
−0.539301 + 0.842113i \(0.681311\pi\)
\(824\) 3.67709e10 0.00277863
\(825\) −2.04455e12 −0.153658
\(826\) −1.45290e11 −0.0108599
\(827\) −2.10229e13 −1.56285 −0.781427 0.623997i \(-0.785508\pi\)
−0.781427 + 0.623997i \(0.785508\pi\)
\(828\) −5.75594e11 −0.0425579
\(829\) −1.46485e13 −1.07720 −0.538602 0.842560i \(-0.681047\pi\)
−0.538602 + 0.842560i \(0.681047\pi\)
\(830\) −9.84005e11 −0.0719691
\(831\) −6.57622e12 −0.478379
\(832\) 6.21724e12 0.449824
\(833\) 7.10916e12 0.511583
\(834\) −2.79026e11 −0.0199709
\(835\) 3.79077e11 0.0269860
\(836\) −1.83292e13 −1.29782
\(837\) −9.95167e10 −0.00700860
\(838\) −7.84714e11 −0.0549684
\(839\) 1.72197e13 1.19976 0.599882 0.800088i \(-0.295214\pi\)
0.599882 + 0.800088i \(0.295214\pi\)
\(840\) −1.25268e12 −0.0868126
\(841\) 8.94024e12 0.616264
\(842\) 5.41784e11 0.0371468
\(843\) −7.10914e12 −0.484834
\(844\) −2.10636e13 −1.42887
\(845\) 1.05181e13 0.709709
\(846\) −3.42343e11 −0.0229771
\(847\) −1.98063e13 −1.32229
\(848\) 4.95190e12 0.328844
\(849\) 2.85447e12 0.188557
\(850\) −2.19039e11 −0.0143925
\(851\) −3.54838e12 −0.231925
\(852\) 4.46964e12 0.290599
\(853\) −3.92321e12 −0.253729 −0.126865 0.991920i \(-0.540491\pi\)
−0.126865 + 0.991920i \(0.540491\pi\)
\(854\) 1.45151e12 0.0933811
\(855\) −4.23743e12 −0.271179
\(856\) −1.57606e12 −0.100332
\(857\) 2.76305e13 1.74975 0.874873 0.484353i \(-0.160945\pi\)
0.874873 + 0.484353i \(0.160945\pi\)
\(858\) −4.25462e11 −0.0268021
\(859\) −2.03071e13 −1.27256 −0.636281 0.771457i \(-0.719528\pi\)
−0.636281 + 0.771457i \(0.719528\pi\)
\(860\) −2.52884e13 −1.57644
\(861\) −7.67568e12 −0.475995
\(862\) −2.75145e11 −0.0169738
\(863\) −1.34096e13 −0.822940 −0.411470 0.911423i \(-0.634984\pi\)
−0.411470 + 0.911423i \(0.634984\pi\)
\(864\) 6.50447e11 0.0397100
\(865\) 2.11174e12 0.128253
\(866\) 2.65156e11 0.0160203
\(867\) 2.68972e12 0.161667
\(868\) −7.30425e11 −0.0436754
\(869\) 2.57684e13 1.53285
\(870\) −7.75671e11 −0.0459030
\(871\) −1.42914e11 −0.00841382
\(872\) 1.98843e12 0.116463
\(873\) −2.21808e12 −0.129245
\(874\) 1.37944e11 0.00799650
\(875\) −2.23470e13 −1.28880
\(876\) −3.17319e12 −0.182066
\(877\) 1.15867e13 0.661399 0.330699 0.943736i \(-0.392715\pi\)
0.330699 + 0.943736i \(0.392715\pi\)
\(878\) 1.99954e12 0.113555
\(879\) −1.06535e13 −0.601926
\(880\) −2.29418e13 −1.28960
\(881\) 1.40889e12 0.0787929 0.0393964 0.999224i \(-0.487456\pi\)
0.0393964 + 0.999224i \(0.487456\pi\)
\(882\) 1.87515e11 0.0104334
\(883\) 4.99843e12 0.276701 0.138350 0.990383i \(-0.455820\pi\)
0.138350 + 0.990383i \(0.455820\pi\)
\(884\) 9.46710e12 0.521413
\(885\) −1.23926e12 −0.0679076
\(886\) −1.31077e12 −0.0714620
\(887\) 1.40515e13 0.762197 0.381099 0.924534i \(-0.375546\pi\)
0.381099 + 0.924534i \(0.375546\pi\)
\(888\) 2.67108e12 0.144155
\(889\) 3.06627e13 1.64646
\(890\) −9.37450e11 −0.0500833
\(891\) 3.02716e12 0.160911
\(892\) 1.18490e13 0.626671
\(893\) −1.70404e13 −0.896701
\(894\) −4.35280e11 −0.0227903
\(895\) 7.76549e12 0.404544
\(896\) 6.36030e12 0.329679
\(897\) −6.65047e11 −0.0342994
\(898\) 1.27732e12 0.0655476
\(899\) −9.06751e11 −0.0462988
\(900\) 1.19997e12 0.0609650
\(901\) 7.46685e12 0.377464
\(902\) 1.36349e12 0.0685840
\(903\) 2.43727e13 1.21986
\(904\) −1.38271e12 −0.0688611
\(905\) 1.10612e13 0.548129
\(906\) −1.08825e12 −0.0536603
\(907\) −2.44121e13 −1.19777 −0.598883 0.800837i \(-0.704389\pi\)
−0.598883 + 0.800837i \(0.704389\pi\)
\(908\) 2.30353e13 1.12463
\(909\) 2.06793e12 0.100461
\(910\) −7.21941e11 −0.0348992
\(911\) −6.54472e12 −0.314817 −0.157409 0.987534i \(-0.550314\pi\)
−0.157409 + 0.987534i \(0.550314\pi\)
\(912\) 1.07056e13 0.512428
\(913\) 3.49902e13 1.66659
\(914\) 1.86936e12 0.0886001
\(915\) 1.23808e13 0.583919
\(916\) −1.46285e13 −0.686548
\(917\) −3.68560e13 −1.72126
\(918\) 3.24309e11 0.0150718
\(919\) −2.52922e13 −1.16968 −0.584841 0.811148i \(-0.698843\pi\)
−0.584841 + 0.811148i \(0.698843\pi\)
\(920\) 3.47829e11 0.0160074
\(921\) −1.81849e12 −0.0832805
\(922\) −2.85987e12 −0.130334
\(923\) 5.16426e12 0.234207
\(924\) 2.22185e13 1.00275
\(925\) 7.39751e12 0.332237
\(926\) −2.55339e11 −0.0114121
\(927\) −1.50779e11 −0.00670627
\(928\) 5.92658e12 0.262324
\(929\) 1.41243e13 0.622151 0.311075 0.950385i \(-0.399311\pi\)
0.311075 + 0.950385i \(0.399311\pi\)
\(930\) 2.99966e10 0.00131492
\(931\) 9.33370e12 0.407174
\(932\) 1.57265e13 0.682747
\(933\) 5.94146e12 0.256700
\(934\) 1.23596e12 0.0531426
\(935\) −3.45934e13 −1.48027
\(936\) 5.00621e11 0.0213190
\(937\) 2.38027e13 1.00878 0.504391 0.863475i \(-0.331717\pi\)
0.504391 + 0.863475i \(0.331717\pi\)
\(938\) −3.59332e10 −0.00151560
\(939\) −2.12767e13 −0.893118
\(940\) −2.14323e13 −0.895353
\(941\) 3.60757e13 1.49990 0.749949 0.661495i \(-0.230078\pi\)
0.749949 + 0.661495i \(0.230078\pi\)
\(942\) 2.94927e11 0.0122035
\(943\) 2.13129e12 0.0877689
\(944\) 3.13090e12 0.128320
\(945\) 5.13660e12 0.209523
\(946\) −4.32951e12 −0.175764
\(947\) 3.64992e13 1.47472 0.737359 0.675501i \(-0.236073\pi\)
0.737359 + 0.675501i \(0.236073\pi\)
\(948\) −1.51238e13 −0.608168
\(949\) −3.66634e12 −0.146735
\(950\) −2.87579e11 −0.0114551
\(951\) 2.70781e13 1.07351
\(952\) 4.77213e12 0.188298
\(953\) −8.43079e12 −0.331093 −0.165547 0.986202i \(-0.552939\pi\)
−0.165547 + 0.986202i \(0.552939\pi\)
\(954\) 1.96950e11 0.00769817
\(955\) 2.11477e13 0.822710
\(956\) −4.24013e13 −1.64179
\(957\) 2.75821e13 1.06298
\(958\) 2.05979e12 0.0790092
\(959\) 5.64010e13 2.15329
\(960\) 1.33336e13 0.506672
\(961\) −2.64046e13 −0.998674
\(962\) 1.53939e12 0.0579510
\(963\) 6.46263e12 0.242154
\(964\) −4.19765e13 −1.56552
\(965\) 2.27686e13 0.845207
\(966\) −1.67215e11 −0.00617841
\(967\) 3.44781e13 1.26802 0.634008 0.773326i \(-0.281409\pi\)
0.634008 + 0.773326i \(0.281409\pi\)
\(968\) −4.13986e12 −0.151547
\(969\) 1.61427e13 0.588192
\(970\) 6.68578e11 0.0242482
\(971\) 1.93005e13 0.696757 0.348378 0.937354i \(-0.386732\pi\)
0.348378 + 0.937354i \(0.386732\pi\)
\(972\) −1.77668e12 −0.0638426
\(973\) 1.68358e13 0.602181
\(974\) −1.46468e12 −0.0521469
\(975\) 1.38646e12 0.0491346
\(976\) −3.12791e13 −1.10339
\(977\) 3.95365e12 0.138827 0.0694133 0.997588i \(-0.477887\pi\)
0.0694133 + 0.997588i \(0.477887\pi\)
\(978\) −1.95184e12 −0.0682211
\(979\) 3.33348e13 1.15978
\(980\) 1.17394e13 0.406562
\(981\) −8.15356e12 −0.281084
\(982\) −1.81223e12 −0.0621889
\(983\) 1.92951e13 0.659106 0.329553 0.944137i \(-0.393102\pi\)
0.329553 + 0.944137i \(0.393102\pi\)
\(984\) −1.60435e12 −0.0545534
\(985\) 1.73676e13 0.587864
\(986\) 2.95495e12 0.0995645
\(987\) 2.06563e13 0.692827
\(988\) 1.24295e13 0.414998
\(989\) −6.76753e12 −0.224930
\(990\) −9.12454e11 −0.0301893
\(991\) 2.76855e13 0.911845 0.455922 0.890020i \(-0.349309\pi\)
0.455922 + 0.890020i \(0.349309\pi\)
\(992\) −2.29191e11 −0.00751441
\(993\) 5.67595e12 0.185254
\(994\) 1.29846e12 0.0421882
\(995\) −5.45981e12 −0.176593
\(996\) −2.05362e13 −0.661232
\(997\) −3.27614e13 −1.05011 −0.525054 0.851069i \(-0.675955\pi\)
−0.525054 + 0.851069i \(0.675955\pi\)
\(998\) 1.13457e12 0.0362030
\(999\) −1.09527e13 −0.347919
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.10.a.a.1.12 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.12 21 1.1 even 1 trivial